Novel hyperbolic and exponential ansatz methods to the fractional fifth-order Korteweg–de Vries equations

Abstract

Abstract This paper aims to investigate the class of fifth-order Korteweg–de Vries equations by devising suitable novel hyperbolic and exponential ansatze. The class under consideration is endowed with a time-fractional order derivative defined in the conformable fractional derivative sense. We realize various solitons and solutions of these equations. The fractional behavior of the solutions is studied comprehensively by using 2D and 3D graphs. The results demonstrate that the methods mentioned here are more effective in solving problems in mathematical physics and other branches of science.

Keywords

• Fractional derivative
• Fifth-order KdV equations
• Hyperbolic wave solutions
• Exponential wave solutions
• Solitary wave solutions